Percentage Change Formula: How to Calculate It (With Examples)
Master the percentage change formula ((new-old)/old x 100) with step-by-step examples for increases, decreases, and negative numbers, plus how it differs from percent difference.
The Percentage Change Formula, Explained Plainly
The percentage change formula is ((new value − old value) / old value) × 100. You subtract the original number from the new number, divide that difference by the original number, then multiply by 100 to turn the result into a percent. A positive answer means the value went up; a negative answer means it went down. That single line is all you need to learn how to calculate percentage change for prices, traffic, weight, test scores, or anything else that moved from one number to another.
Here is the formula working in practice. If a price rose from 50 to 65, you compute (65 − 50) / 50 × 100 = 30%, an increase. If website visits dropped from 1,200 to 900, you compute (900 − 1,200) / 1,200 × 100 = −25%, a decrease. The negative sign is the answer doing its job, not a mistake. If you would rather skip the arithmetic entirely, our free Percentage Calculator does every step in your browser with no signup.
How to Calculate Percentage Change Step by Step
Most mistakes with the percent change formula come from rushing or dividing by the wrong number. Slow it down into four steps and it becomes mechanical:
- Identify the old value and the new value. The old value is where you started (the earlier or original figure). The new value is where you ended up.
- Subtract the old value from the new value. This difference can be positive or negative, and that sign matters.
- Divide the difference by the old value. Always divide by the original number, never the new one. This is the step people get wrong most often.
- Multiply by 100. This converts the decimal into a percentage you can read and report.
Written as one expression: percentage change = (new − old) ÷ old × 100. Keep the old value in the denominator and the rest takes care of itself.
A worked-example table
The fastest way to internalize the percentage change formula is to see it run across several scenarios, including ones with negative numbers. Each row below uses the exact same four steps.
| Scenario | Old value | New value | Difference (new − old) | Calculation | Result |
|---|---|---|---|---|---|
| Price increase | 50 | 65 | +15 | (15 / 50) × 100 | +30% (increase) |
| Traffic decrease | 1,200 | 900 | −300 | (−300 / 1,200) × 100 | −25% (decrease) |
| Salary raise | 40,000 | 44,000 | +4,000 | (4,000 / 40,000) × 100 | +10% (increase) |
| Doubling | 20 | 40 | +20 | (20 / 20) × 100 | +100% (increase) |
| Temperature drop (negatives) | −5 | −15 | −10 | (−10 / −5) × 100 | −200% (decrease) |
| Recovery from a loss | −10 | 5 | +15 | (15 / −10) × 100 | −150% (sign flips) |
Notice the last two rows. When the old value is negative, the result can look counterintuitive because dividing by a negative number flips the sign. This is the single biggest reason analysts caution against percentage change when the starting figure is negative or crosses zero, a point worth keeping in mind for financial reporting.
Percentage Increase Formula vs Percentage Decrease
People often search for the percentage increase formula and the percentage decrease formula as if they were two different equations. They are not. It is the same formula every time; the only thing that changes is the sign of the answer.
- Percentage increase: the new value is larger than the old value, so (new − old) is positive and you get a positive percent. Going from 80 to 100 gives (100 − 80) / 80 × 100 = +25%.
- Percentage decrease: the new value is smaller than the old value, so (new − old) is negative and you get a negative percent. Going from 100 to 80 gives (80 − 100) / 100 × 100 = −20%.
Look closely at those two examples. An increase from 80 to 100 is +25%, but the matching decrease from 100 to 80 is only −20%. The percentages are not symmetric because the denominator (the old value) is different in each direction. This asymmetry surprises people constantly, and it is why a 50% loss needs a 100% gain to break even, not another 50%.
Reporting decreases without the minus sign
In everyday writing you usually drop the negative sign and say the magnitude in words instead. So "−25%" becomes "a 25% decrease" or "fell by 25%." The math is identical; you are just describing the direction with language rather than a symbol. Keep the sign when you are feeding numbers into a spreadsheet or chart, and switch to plain words when you are writing a sentence a human will read.
Percent Change Formula vs Percent Difference
Percentage change and percent difference sound alike but answer different questions, and mixing them up produces wrong numbers. Percentage change has a clear before and after, so it divides by the original value. Percent difference compares two values where neither is "first," so it divides by their average.
| Measure | When to use it | Denominator | Formula |
|---|---|---|---|
| Percentage change | One value changed over time (before vs after) | Old value | (new − old) / old × 100 |
| Percent difference | Comparing two independent values, no order | Average of the two | |A − B| / ((A + B) / 2) × 100 |
Quick gut check: if you can naturally say "it went from X to Y," use percentage change. If you would say "X compared to Y" with no implied direction, percent difference is the right tool. For example, last month's revenue versus this month's revenue is a change. Lab result A versus lab result B from two different machines is a difference.
Real-World Uses of the Percentage Change Formula
This one formula quietly powers a huge share of everyday number work. A few places it shows up:
- Prices and discounts. Tracking how much a product's price rose or how deep a sale cut into the original. When the new value is a sale price, the negative percent is the discount. Our Discount Calculator turns that into the final price and amount saved automatically.
- Business metrics. Month-over-month revenue, week-over-week signups, year-over-year growth. Analysts live in this formula.
- Personal finance. Investment returns, the change in a bill, or how much a paycheck grew after a raise.
- Health and fitness. Weight change, resting heart rate, or strength gains between two test dates.
- Academics. Score improvement between two exams, expressed as a percent of the earlier score.
When you are averaging several of these changes together, watch out: you generally cannot just average the percentages to get a true overall rate. If you need the mean of a set of numbers first, use our Average Calculator, then compute the change on those averages. For more browser-based math tools, browse the full Online Calculators hub.
Doing it in a spreadsheet
In Excel or Google Sheets, if your old value is in cell A2 and the new value in B2, the formula is =(B2-A2)/A2. Format the cell as a percentage and the tool multiplies by 100 and adds the percent sign for you, so you skip the last step by hand. Drag it down a column and you have a change figure for every row in seconds.
Common Mistakes That Throw Off Percentage Change
Even people comfortable with the percent change formula trip on the same handful of errors. Watch for these:
- Dividing by the new value. The denominator is always the old value. Divide by the new one and every answer is wrong.
- Reversing old and new. Swapping them flips the sign and changes the size of the percentage, since the denominators differ.
- Confusing percentage points with percent. If an interest rate moves from 4% to 6%, that is a 2 percentage point rise but a 50% increase. They are not the same statement.
- Trusting percentage change when the base is near zero. A tiny old value makes the percentage explode, and a base of exactly zero makes the formula undefined because you cannot divide by zero.
- Averaging percentages directly. A 50% gain followed by a 50% loss does not net to zero; it leaves you down 25%.
Rule of thumb: if your old value is zero, negative, or close to zero, report the raw difference instead of a percentage. Percentage change only behaves well when the starting point is a clear, positive baseline.
Calculate It Instantly Instead of by Hand
Once you understand the mechanics, there is no reason to do the arithmetic manually every time. Plug your old and new values into the free Percentage Calculator and it returns the percentage change, the direction, and the raw difference in one click, right in your browser with nothing to install and no account. It is the quickest way to apply the percentage change formula to real numbers without second-guessing your division.
If you are crunching numbers across different units, a couple of related guides pair well with this one: our walkthrough of the hours calculator for time-based math, and the stopwatch guide for measuring elapsed intervals you might then compare as a percentage change.
Frequently Asked Questions
What is the percentage change formula?
The percentage change formula is ((new value − old value) / old value) × 100. Subtract the original value from the new value, divide by the original value, then multiply by 100. A positive result is an increase and a negative result is a decrease.
How do I calculate percentage increase?
Use the same formula. Because the new value is larger than the old value, the result comes out positive. For example, from 200 to 250: (250 − 200) / 200 × 100 = 25%, a 25% increase.
How do I calculate percentage decrease?
Again, the same formula. The new value is smaller, so the result is negative. From 250 to 200: (200 − 250) / 250 × 100 = −20%, which you would report as a 20% decrease.
Why is a percentage increase and decrease between the same two numbers not equal?
Because the denominator changes. Going up from 80 to 100 divides by 80 (+25%), while coming down from 100 to 80 divides by 100 (−20%). Different starting points produce different percentages even though the absolute change is the same 20 units.
What is the difference between percentage change and percent difference?
Percentage change has a clear before and after and divides by the original value. Percent difference compares two values with no implied order and divides by their average: |A − B| / ((A + B) / 2) × 100. Use change for over-time comparisons and difference for side-by-side ones.
Can the percentage change be more than 100%?
Yes. If a value more than doubles, the increase exceeds 100%. Going from 20 to 60 is a 200% increase. A decrease, however, cannot go below −100% for a positive starting value, since the value can only fall to zero.
What happens if the old value is zero?
The formula is undefined because you cannot divide by zero. When the starting value is zero, report the absolute change in raw numbers instead of a percentage, or describe the move in words.
How do I calculate percentage change with negative numbers?
The formula still works, but dividing by a negative old value can flip the sign, so the result may read oddly. For figures that are negative or cross zero, many analysts prefer to report the raw difference rather than a percentage to avoid misleading readers.